Proposition 2.2 ([1]})  All coefficients \({a}_{n,j}(s)\)  of the monic matrix-valued orthogonal polynomials are real matrices. Additionally we have
\({Y}^{(n)}_{-1}(s) = \left( \begin{matrix}{a}_{n,n-1}(s) & -\dfrac{1}{2 \pi i} {\gamma }_n^{-1}(s) \vspace{2.84526pt}\\-2\pi i {\gamma }_{n-1}(s) & -{a}^*_{n,n-1}(s)\end{matrix}\right). \) 

